Furthermore, one may be tempted to view problem REF  as a penalty reformulation of either of the other two problems.
However, while a solution \(x^*\)  of REF  always is a solution of the other two problems with \(\kappa := \Vert x^*\Vert _0\)  or \(\delta := f(x^*)\) , respectively, the opposite implication is in general not true.
This means that solutions of the cardinality-constrained problem or cardinality minimization problem cannot always be recovered as solutions of REF .
More details on these relations can be found in [1]}.
